She added that Spicer, who recently announced that he's stepping down from his post as White House press secretary, and Reince Priebus, Trump's recently ousted chief of staff, would be leading the transition.

"Mike Pence is somewhere planning an inauguration," Waters tweeted. "Priebus and Spicer will lead the transition."

Spicer responded in a tweet on Monday, saying that he would "proudly play any role he asks" should Pence decide to run on in 2024.

"When and if @mike_pence runs in 2024 I would proudly play any role he asks," Spicer tweeted. "Good to know you have already conceded that."

Spicer and Priebus, who previously worked together at the Republican National Committee, didn't last long in Trump's White House. But Pence is more popular with establishment Republicans. He hasn't announced any intention to run for president in 2024.